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Stable and unstable tiling patterns of ABC miktoarm triblock terpolymers studied via GPU-accelerated self-consistent field calculations




Hawthorne, Cody, author
Wang, David, advisor
Bailey, Travis, committee member
Miyake, Garrett M., committee member
Szamel, Grzegorz, committee member

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Block copolymers are macromolecules formed from linking together two or more chemically distinct types of polymers. Provided the different monomers that make up each polymer are immiscible enough, melts of these molecules will self-assemble into highly ordered, periodic structures at length scales typically on the order of nanometers. The exemplary and simplest material in this respect is the AB diblock copolymer, a linear macromolecule formed by bonding together two immiscible polymers (or 'blocks') A and B. This material is capable of assembling into lamellar, cylindrical, spherical, and networked morphologies depending on the length of the A block and degree of immiscibility between A and B. The ability to control bulk properties of block copolymers via tuning these molecular properties, as well as the length scales that these ordered structures form at, makes them intriguing candidates for next generation technological applications in lithography, photonics, and transport. In order to realize these applications it is imperative to have an intimate understanding of the phase behavior of the materials such that the morphology that will form at a given combination of parameters can be predicted reliably. Self-consistent field theory, or SCFT, has emerged as a useful theory for investigating block copolymer phase behavior. This statistical-mechanical theory has been successfully used to construct phase diagrams of the self-assembled morphologies of various block copolymer systems. These phase diagrams provide the connection between molecular properties (such as block lengths, block incompatibility, and chain architecture) and bulk properties necessary in order to control the behavior of the material. The theory must, in general, be solved numerically – an open-source software termed 'PSCFPP' has recently been made available for this purpose, capable of implementing high-performance SCFT calculations for arbitrarily complex acyclic block copolymers by taking advantage of the massive parallelization of GPUs. In this work, PSCFPP is used to apply SCFT to a neat melt of complex ABC miktoarm triblock terpolymers, which are an interesting class of block copolymer formed by linking three distinct polymers A, B, and C at a single junction point. The resulting star-shaped macromolecule is referred to as a 'miktoarm' and exhibits unique morphologies such as the Archimedean tiling patterns that cannot be found in other block copolymer materials. To focus on the effect of composition, which has not yet been fully elucidated, we restrict the interaction parameters between monomers ABC to the symmetric case where all are equivalent. The central region of the phase diagram, where the effect of the miktoarm architecture is most significant, is mapped out in detail and a 3D morphology previously thought to be metastable is shown to be a stable phase. Further, discrepancies in the literature concerning the stability of multiple 2D tiling patterns are resolved such that the phase diagram presented is the most accurate for the system to date. Finally, a 2D morphology of some interest owing to the possibility of exhibiting photonic band gaps is definitively shown to be stable in this system and its thermodynamic properties analyzed to ascertain what drives its formation. These results provide a solid foundation for further refinement of our understanding of ABC miktoarm phase behavior and demonstrate the utility of a software such as PSCFPP for obtaining high-accuracy SCF results.


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